Question: Simplify the following expression: $r = \dfrac{y^2 - y - 12}{y - 4} $
First factor the polynomial in the numerator. $ y^2 - y - 12 = (y - 4)(y + 3) $ So we can rewrite the expression as: $r = \dfrac{(y - 4)(y + 3)}{y - 4} $ We can divide the numerator and denominator by $(y - 4)$ on condition that $y \neq 4$ Therefore $r = y + 3; y \neq 4$